Models of Quantum Dissipation
The main problem to address to study dissipation at the quantum level is the way to envisage the mechanism of irreversible loss of energy. Quantum mechanics usually deal with the Hamiltonian formalism, where the total energy of the system is a conserved quantity. So in principle it would not be possible to describe dissipation in this framework.
The idea to overcome this issue consists on splitting the total system in two parts: the quantum system where dissipation occurs, and a so-called environment or bath where the energy of the former will flow towards. The way both systems are coupled depends on the details of the microscopic model, and hence, the description of the bath. To include an irreversible flow of energy (i.e., to avoid Poincaré recurrences in which the energy eventually flows back to the system), requires that the bath contain an infinite number of degrees of freedom. Notice that by virtue of the principle of universality, it is expected that the particular description of the bath will not affect the essential features of the dissipative process, as far as the model contains the minimal ingredients to provide the effect.
The simplest way to model the bath was proposed by Feynman and Vernon in a seminal paper from 1963. In this description the bath is a sum of an infinite number of harmonic oscillators, that in quantum mechanics represents a set of free bosonic particles.
Read more about this topic: Quantum Dissipation
Famous quotes containing the words models of, models, quantum and/or dissipation:
“Today it is not the classroom nor the classics which are the repositories of models of eloquence, but the ad agencies.”
—Marshall McLuhan (1911–1980)
“French rhetorical models are too narrow for the English tradition. Most pernicious of French imports is the notion that there is no person behind a text. Is there anything more affected, aggressive, and relentlessly concrete than a Parisan intellectual behind his/her turgid text? The Parisian is a provincial when he pretends to speak for the universe.”
—Camille Paglia (b. 1947)
“The receipt to make a speaker, and an applauded one too, is short and easy.—Take of common sense quantum sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“But there are other things than dissipation that thicken the features. Tears, for example.”
—Rebecca West (1892–1983)